A 'fast-food approach' to the standardization of quadratic diversity

Intuitively, a community composed of ecologically dissimilar taxa is more diverse than a community composed of more similar taxa. However, since traditional diversity indices such as Shannon's entropy or Simpson's diversity are computed solely from the relative abundances of a given species assemblage, they cannot account for ecological differences between species. There have been recent developments regarding the use of quadratic entropy, a diversity index that incorporates both species relative abundances and a measure of the pairwise ecological differences between species. In this paper we firstly show that under some specific circumstances quadratic entropy can be additively decomposed into alpha- beta- and gamma-diversities, a property that renders it a desirable measure of diversity in the ecological practice. Next, we suggest a quick and simple method for obtaining a standardized version of quadratic entropy that may allow an easier interpretation of the resulting diversity values.